Analysis of etching at a solid-solid interface

Abstract

We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height variance (roughness). We apply this method to the etching model in 1 + 1 dimensions, and then we obtain the roughness exponent. Using this in conjunction with the Galilean invariance we obtain the other exponents, which perfectly match the numerical results obtained from simulations. These exponents are exact, and they are the same as those exhibited by the Kardar-Parisi-Zhang (KPZ) model for this dimension. Therefore, our results provide proof for the conjecture that the etching and KPZ models belong to the same universality class. Moreover, the method is general, and it can be applied to other cellular automata models.

References in corpus (6)

• Random deposition of particles of different sizes
• Growth exponents of the etching model in high dimensions
• Stochastic Model in the Kardar-Parisi-Zhang Universality With Minimal Finite Size Effects
• Maximal and minimal height distributions of fluctuating interfaces
• A random rule model of surface growth
• Revisiting random deposition with surface relaxation: approaches from growth rules to Edwards-Wilkinson equation

Cited by in corpus (1)

• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain